Mathematical Foundations of Parity Logic
This chapter provides a compact survey of the binary space B n and related concepts, in particular the eXclusive-OR operation x ⊕ y and its generalization to the binary scalar integral ⊕ i n =1 x i and the binary vector integral ⊕ i n =1 x i for vectors x ∈ B n . We present these mathematical foundations in standard computer science nomenclature, but we will refer also to the nomenclature of APL, because the binary vector integral in section 2.3 has its origin in APL ([IVE62], [IVE78], [LAN93], [LOC89], [ZA95]).
KeywordsBinary Vector Parity Logic Mathematical Foundation Symmetry Operator Boolean Ring
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